Abstract

We analyze the first-order design of light sources consisting of multiple light-emitting diodes (LEDs) to uniformly illuminate a near target plane by considering each single LED as an imperfect Lambertian emitter. Simple approximate equations and formulas are derived for the optimum LED-to-LED spacing, i.e., the optimum packaging density, of several array configurations to achieve uniform near-field irradiance.

© 2006 Optical Society of America

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  1. Y. Narukawa, "White-light LEDs," Opt. Photon. News 15, 24-29 (2004).
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  2. J. Wafer, "LEDs continue to advance," Photonics Spectra 39, 60-62 (2005).
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    [CrossRef]
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  5. H. Yamamoto, M. Kouno, S. Muguruma, Y. Hayasaki, Y. Nagai, Y. Shimizu, and N. Nishida, "Enlargement of viewing area of stereoscopic full-color LED display by use of a parallax barrier," Appl. Opt. 41, 6907-6919 (2002).
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    [CrossRef]
  7. L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
    [CrossRef]
  8. L. Repetto, E. Piano, and C. Pontiggia, "Lensless digital holographic microscope with light-emitting diode illumination," Opt. Lett. 29, 1132-1134 (2004).
    [CrossRef] [PubMed]
  9. C. Deller, G. Smith, and J. Franklin, "Colour mixing LEDs with short microsphere doped acrylic rods," Opt. Express 12, 3327-3333 (2004).
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  16. J. M. Benavides and R. H. Webb, "Optical characterization of ultrabright LEDs," Appl. Opt. 44, 4000-4003 (2005).
    [CrossRef] [PubMed]
  17. W. J. Cassarly, "LED modelling: pros and cons of common methods," Photon. Tech Briefs , pp IIa-2a (April 2002), special supplement to NASA Tech Briefs.
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  19. I. Moreno and L. M. Molinar, "Color uniformity of the light distribution from several cluster configurations of multicolor LEDs," in Fifth International Conference on Solid State Lighting, I. T. Ferguson, J. C. Carrano, T. Taguchi, I. E. Ashdown, eds., Proc. SPIE 5941, 359-365 (2005).

2005

J. Wafer, "LEDs continue to advance," Photonics Spectra 39, 60-62 (2005).

A. L. Dubovikov, S. S. Repin, and S. N. Natarovskii, "Features of the use of LEDs in artificial-vision systems," J. Opt Technol. 72, 40-42 (2005).
[CrossRef]

J. M. Benavides and R. H. Webb, "Optical characterization of ultrabright LEDs," Appl. Opt. 44, 4000-4003 (2005).
[CrossRef] [PubMed]

F. Hu, K. Y. Qian, and Y. Luo, "Far-field pattern simulation of flip-chip bonded power light-emitting diodes by a Monte Carlo photon-tracing method," Appl. Opt. 44, 2768-2771 (2005).
[CrossRef] [PubMed]

I. Moreno and L. M. Molinar, "Color uniformity of the light distribution from several cluster configurations of multicolor LEDs," in Fifth International Conference on Solid State Lighting, I. T. Ferguson, J. C. Carrano, T. Taguchi, I. E. Ashdown, eds., Proc. SPIE 5941, 359-365 (2005).

2004

Y. Narukawa, "White-light LEDs," Opt. Photon. News 15, 24-29 (2004).
[CrossRef]

I. Moreno and R. I. Tzonchev, "Effects on illumination uniformity due to dilution on arrays of LEDs," in Nonimaging Optics and Efficient Illumination Systems, R. Winston, R. J. Koshel, eds., Proc. SPIE 5529, 268-275 (2004).
[CrossRef]

T. Ito and K. Okano, "Color electroholography by three colored reference lights simultaneously incident upon one hologram panel," Opt. Express 12, 4320-4325 (2004).
[CrossRef] [PubMed]

L. Repetto, E. Piano, and C. Pontiggia, "Lensless digital holographic microscope with light-emitting diode illumination," Opt. Lett. 29, 1132-1134 (2004).
[CrossRef] [PubMed]

C. Deller, G. Smith, and J. Franklin, "Colour mixing LEDs with short microsphere doped acrylic rods," Opt. Express 12, 3327-3333 (2004).
[CrossRef] [PubMed]

J. F. Van Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. 43, 1503-1510 (2004).
[CrossRef]

2003

2002

2001

Y. Kawakami, J. Shimada, and S. Fujita, "Fabrication of LED lighting goggle for surgical operation and approach toward high color rendering performance," in Solid State Lighting and Displays, I. T. Ferguson, Y. S. Park, N. Narendran, and S. P. DenBaars, eds., Proc. SPIE 4445, 156-164 (2001).
[CrossRef]

2000

L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
[CrossRef]

1999

Benavides, J. M.

Carey, J. J.

Cassarly, W. J.

W. J. Cassarly, "LED modelling: pros and cons of common methods," Photon. Tech Briefs , pp IIa-2a (April 2002), special supplement to NASA Tech Briefs.

Causa, F.

Deller, C.

DeVelis, J. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook (SPIE Press, 1989), pp. 38-45.
[CrossRef]

Domjan, L.

L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
[CrossRef]

Dubovikov, A. L.

A. L. Dubovikov, S. S. Repin, and S. N. Natarovskii, "Features of the use of LEDs in artificial-vision systems," J. Opt Technol. 72, 40-42 (2005).
[CrossRef]

Feiten, W.

L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
[CrossRef]

Franklin, J.

Fujita, S.

Y. Kawakami, J. Shimada, and S. Fujita, "Fabrication of LED lighting goggle for surgical operation and approach toward high color rendering performance," in Solid State Lighting and Displays, I. T. Ferguson, Y. S. Park, N. Narendran, and S. P. DenBaars, eds., Proc. SPIE 4445, 156-164 (2001).
[CrossRef]

Girkin, J. M.

Hayasaki, Y.

Hough, T. A.

J. F. Van Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. 43, 1503-1510 (2004).
[CrossRef]

Hu, F.

Ito, T.

Kawakami, Y.

Y. Kawakami, J. Shimada, and S. Fujita, "Fabrication of LED lighting goggle for surgical operation and approach toward high color rendering performance," in Solid State Lighting and Displays, I. T. Ferguson, Y. S. Park, N. Narendran, and S. P. DenBaars, eds., Proc. SPIE 4445, 156-164 (2001).
[CrossRef]

Kocsanyi, L.

L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
[CrossRef]

Kouno, M.

Luo, Y.

Molinar, L. M.

I. Moreno and L. M. Molinar, "Color uniformity of the light distribution from several cluster configurations of multicolor LEDs," in Fifth International Conference on Solid State Lighting, I. T. Ferguson, J. C. Carrano, T. Taguchi, I. E. Ashdown, eds., Proc. SPIE 5941, 359-365 (2005).

Moreno, I.

I. Moreno and L. M. Molinar, "Color uniformity of the light distribution from several cluster configurations of multicolor LEDs," in Fifth International Conference on Solid State Lighting, I. T. Ferguson, J. C. Carrano, T. Taguchi, I. E. Ashdown, eds., Proc. SPIE 5941, 359-365 (2005).

I. Moreno and R. I. Tzonchev, "Effects on illumination uniformity due to dilution on arrays of LEDs," in Nonimaging Optics and Efficient Illumination Systems, R. Winston, R. J. Koshel, eds., Proc. SPIE 5529, 268-275 (2004).
[CrossRef]

Muguruma, S.

Nagai, Y.

Narukawa, Y.

Y. Narukawa, "White-light LEDs," Opt. Photon. News 15, 24-29 (2004).
[CrossRef]

Natarovskii, S. N.

A. L. Dubovikov, S. S. Repin, and S. N. Natarovskii, "Features of the use of LEDs in artificial-vision systems," J. Opt Technol. 72, 40-42 (2005).
[CrossRef]

Nishida, N.

Okano, K.

Parrent, G. B.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook (SPIE Press, 1989), pp. 38-45.
[CrossRef]

Piano, E.

Pontiggia, C.

Qian, K. Y.

Repetto, L.

Repin, S. S.

A. L. Dubovikov, S. S. Repin, and S. N. Natarovskii, "Features of the use of LEDs in artificial-vision systems," J. Opt Technol. 72, 40-42 (2005).
[CrossRef]

Reynolds, G. O.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook (SPIE Press, 1989), pp. 38-45.
[CrossRef]

Richter, P.

L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
[CrossRef]

Sarma, J.

Shimada, J.

Y. Kawakami, J. Shimada, and S. Fujita, "Fabrication of LED lighting goggle for surgical operation and approach toward high color rendering performance," in Solid State Lighting and Displays, I. T. Ferguson, Y. S. Park, N. Narendran, and S. P. DenBaars, eds., Proc. SPIE 4445, 156-164 (2001).
[CrossRef]

Shimizu, Y.

Smith, G.

Thompson, B. J.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook (SPIE Press, 1989), pp. 38-45.
[CrossRef]

Tzonchev, R. I.

I. Moreno and R. I. Tzonchev, "Effects on illumination uniformity due to dilution on arrays of LEDs," in Nonimaging Optics and Efficient Illumination Systems, R. Winston, R. J. Koshel, eds., Proc. SPIE 5529, 268-275 (2004).
[CrossRef]

Van Derlofske, J. F.

J. F. Van Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. 43, 1503-1510 (2004).
[CrossRef]

Varkonyi, S.

L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
[CrossRef]

Wafer, J.

J. Wafer, "LEDs continue to advance," Photonics Spectra 39, 60-62 (2005).

Webb, R. H.

Whitters, C. J.

Wood, D.

D. Wood, Optoelectronic Semiconductor Devices (Prentice-Hall International, 1994), pp. 84-88.

Yamamoto, H.

Appl. Opt.

J. Opt Technol.

A. L. Dubovikov, S. S. Repin, and S. N. Natarovskii, "Features of the use of LEDs in artificial-vision systems," J. Opt Technol. 72, 40-42 (2005).
[CrossRef]

Opt. Eng.

L. Domjan, L. Kocsanyi, P. Richter, S. Varkonyi, and W. Feiten, "Stripe illuminator based on LED array and parabolic mirror for active triangulation sensors used on mobile robots," Opt. Eng. 39, 2867-2875 (2000).
[CrossRef]

J. F. Van Derlofske and T. A. Hough, "Analytical model of flux propagation in light-pipe systems," Opt. Eng. 43, 1503-1510 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photon. News

Y. Narukawa, "White-light LEDs," Opt. Photon. News 15, 24-29 (2004).
[CrossRef]

Photon. Tech Briefs

W. J. Cassarly, "LED modelling: pros and cons of common methods," Photon. Tech Briefs , pp IIa-2a (April 2002), special supplement to NASA Tech Briefs.

Photonics Spectra

J. Wafer, "LEDs continue to advance," Photonics Spectra 39, 60-62 (2005).

Proc. SPIE

I. Moreno and R. I. Tzonchev, "Effects on illumination uniformity due to dilution on arrays of LEDs," in Nonimaging Optics and Efficient Illumination Systems, R. Winston, R. J. Koshel, eds., Proc. SPIE 5529, 268-275 (2004).
[CrossRef]

I. Moreno and L. M. Molinar, "Color uniformity of the light distribution from several cluster configurations of multicolor LEDs," in Fifth International Conference on Solid State Lighting, I. T. Ferguson, J. C. Carrano, T. Taguchi, I. E. Ashdown, eds., Proc. SPIE 5941, 359-365 (2005).

Y. Kawakami, J. Shimada, and S. Fujita, "Fabrication of LED lighting goggle for surgical operation and approach toward high color rendering performance," in Solid State Lighting and Displays, I. T. Ferguson, Y. S. Park, N. Narendran, and S. P. DenBaars, eds., Proc. SPIE 4445, 156-164 (2001).
[CrossRef]

Other

D. Wood, Optoelectronic Semiconductor Devices (Prentice-Hall International, 1994), pp. 84-88.

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook (SPIE Press, 1989), pp. 38-45.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Two-LED array. (a) Schematic illustration of the LED array with a screen at a distance z. (b) The uniform irradiance distribution (normalized to its maximum value) along the x direction at y = 0 for m = 80.7 and d = d 0 = 0.219. The dotted curves show the irradiance patterns of each single LED. (c) Corresponding pattern when the separation between LEDs is slightly increased.

Fig. 2
Fig. 2

Circular ring LED array. (a) Schematic illustration of an array with N = 6. (b) The uniform irradiance distribution of this array when m = 30 and ρ = ρ0 = 0.25. (c) Corresponding normalized irradiance graph along the x direction at y = 0.

Fig. 3
Fig. 3

Circular ring LED array with one LED in the center. (a) Schematic illustration of an array with (N + 1) = 7. (b) The uniform irradiance distribution of this array when m = 30, ρ = ρ0 = 0.354, and ϕ0 = 0.72. (c) Corresponding normalized irradiance graph along the x direction at y = 0.

Fig. 4
Fig. 4

Linear array of LEDs. (a) Schematic illustration of an array with N = 7. (b) The uniform irradiance distribution of this array when m = 80.7 and d = d 0 = 0.135. (c) Resulting normalized irradiance graph along the x direction at y = 0.

Fig. 5
Fig. 5

Uniform irradiance pattern (along the x direction at y = 0) for a linear array of three LEDs with m = 30, d = d 0 = 0.603, and ϕ0 = 0.835.

Fig. 6
Fig. 6

Square array of LEDs. (a) Schematic illustration of an array with N = 7 and M = 7. (b) The uniform irradiance pattern when m = 50 and d = d 0 = 0.17. (c) Corresponding normalized irradiance distribution along the x direction at y = 0.

Fig. 7
Fig. 7

Triangular array of LEDs. (a) Schematic illustration of an array with 46 LEDs (N = 7 and M = 7). (b) The uniform irradiance pattern when m = 50 and d = d 0 = 0.192. (c) Corresponding normalized irradiance distribution along the x direction at y = 0.

Fig. 8
Fig. 8

Relative power distribution plot. The curve indicates the fraction of power of the total flux in an illuminated pattern that falls within a square (for the square array) or a rectangle (for the triangular array).

Fig. 9
Fig. 9

Experimental irradiance distribution of a linear array of LEDs with N = 4. (a) The irradiance pattern when m = 64.66 and d = d 0. (b) Resulting normalized irradiance distribution along the x direction at y = 0.

Equations (22)

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E ( r , θ ) = E 0 ( r ) cos m θ ,
m = ln 2 ln ( cos θ 1 / 2 ) .
E ( x , y , z ) = z m L LED A LED [ ( x x 0 ) 2 + ( y y 0 ) 2 + z 2 ] ( m + 2 ) / 2 ,
E ( x , y , z ) = z m A LED L LED { [ ( x d 2 ) 2 + y 2 + z 2 ] ( m + 2 ) / 2 + [ ( x + d 2 ) 2 + y 2 + z 2 ] ( m + 2 ) / 2 } .
d 0 = 4 m + 3 z ,
E ( x , y , z ) = z m A LED L LED n = 1 N { [ x ρ cos ( 2 π n N ) ] 2 + [ y ρ sin ( 2 π n N ) ] 2 + z 2 } ( m + 2 ) / 2 .
ρ 0 = 2 m + 2 z .
ρ 0 = 1.851 m + 2.259 z .
E ( x , y , z ) = z m A LED L LED ( n = 1 N { [ x ρ cos ( 2 π n N ) ] 2 + [ y ρ sin ( 2 π n N ) ] 2 + z 2 } ( m + 2 ) / 2 + ϕ { x 2 + y 2 + z 2 } ( m + 2 ) / 2 ) ,
ρ 0 = 4 m + 2 z .
ϕ 0 = N ( m + 2 m + 6 ) ( m + 6 ) / 2 .
E ( x , y , z ) = z m A LED L LED n = 1 N { [ x ( N + 1 2 n ) ( d / 2 ) ] 2 + y 2 + z 2 } ( m + 2 ) / 2 .
f ( D ) = n = 1 N [ ( N + 1 2 n ) 2 ( D 2 / 4 ) + 1 ] ( m + 6 ) / 2 [ 1 ( m + 3 ) ( N + 1 2 n ) 2 ( D 2 / 4 ) ] ,
d 0 = 3.2773 m + 4.2539 z .
d 0 = 12 m + 3 z .
ϕ 0 = 4 ( m + 3 m + 6 ) ( m + 6 ) / 2 .
E ( x , y , z ) = z m A LED L LED i = 1 N j = 1 M { [ x ( N + 1 2 i ) ( d / 2 ) ] 2 + [ y ( M + 1 2 j ) ( d / 2 ) ] 2 + z 2 } ( m + 2 ) / 2 .
f ( D ) = i = 1 N j = 1 M ( { [ ( N + 1 2 i ) 2 + ( M + 1 2 j ) 2 ] ( D 2 / 4 ) + 1 } ( m + 6 ) / 2 { 1 [ ( m + 3 ) ( N + 1 2 i ) 2 - ( M + 1 2 j ) 2 ] ( D 2 / 4 ) } ) ,
d 0 = 4 m + 2 z .
d 0 = 1.2125 m 3.349 z .
E ( x , y , z ) = z m A LED L LED j = 1 M i = 1 N - { [ x ( N + 2 i ) ( d / 2 ) ] 2 + [ y ( M + 1 2 j ) ( 3 d / 4 ) ] 2 + z 2 } ( m + 2 ) / 2 ,
f ( D ) = j = 1 M i = 1 N - ( { [ ( N + 2 i ) 2 + 3 / 4 ( M + 1 2 j ) 2 ] ( D 2 / 4 ) + 1 } ( m + 6 ) / 2 { 1 [ ( m + 3 ) ( N + 2 i ) 2 - 3 / 4 ( M + 1 2 j ) 2 ] ( D 2 / 4 ) } ) ,

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